Abstract

The free-propagation features of light beams whose transverse electric field lines are logarithmic spirals (namely, spirally polarized beams) are investigated in both the paraxial and the nonparaxial regime. The complete propagated electric field is considered, and some general properties are obtained regardless of the specific transverse distribution. Simple and significant analytical results are obtained when the transverse intensity profile is chosen as that pertinent to an axially symmetric Laguerre–Gaussian beam of order 1 (namely, spirally polarized donut beams). In particular, it is found that for such beams, the propagated longitudinal electric field can be expressed as a simple superposition of elegant Laguerre–Gaussian beams. Numerical results are presented for different values of the beam parameters and are compared with recently obtained experimental results.

Modulus of the normalized longitudinal on-axis electric field for a SPDB. Curves refer to different values of β=πw/λ and are drawn as functions of z/zR, where zR=πw2/λ. Dots represent the paraxial solution.

Modulus of the relative difference between the exact expression of the longitudinal on-axis electric field for a SPDB and its paraxial approximation. Curves refer to different values of β=πw/λ and are plotted as functions of z/zR, where zR=πw2/λ.

Behaviors of |E⊥| and |Ez|, for the case of a radially polarized beam (α=0), as functions of the normalized transverse coordinate r/w, evaluated at the transverse plane z=zR through the paraxial approximation (m=0) (circles), by adding the first-order (m=1) nonparaxial correction (triangles) and by adding also the second-order (m=2) nonparaxial correction (solid curve) for a SPDB with (a), (b) β=2; (c), (d) β=3; (e, f) β=4; and (g), (h) β=5.

Intensity profiles, evaluated across the plane z=0 as functions of the lateral position, pertinent to the transverse (dotted curve), longitudinal (triangles), and total (solid curve) electric fields, for the case of a radially polarized beam (α=0) with β≃2.3, to be compared with the experimental results shown in Fig. 3(d) of Ref. 14. Wavelength is λ=632.8nm.